Ray Optics and Optical Instruments

Ray Optics and Optical Instruments treats light as rays travelling in straight lines and uses simple geometry to explain how mirrors, lenses and prisms form images. In this chapter you will study reflection by spherical mirrors with the Cartesian sign convention, derive the mirror formula 1/v + 1/u = 1/f and find magnification. You will revise refraction and Snell's law, explain apparent depth, and study total internal reflection with applications such as optical fibres, sparkling diamonds and mirages. You will derive the formula for refraction at a spherical surface, the lens maker's formula and the thin lens formula 1/v - 1/u = 1/f, and calculate the power of a lens and of lenses in contact. The chapter explains refraction through a prism and the relation between refractive index, angle of prism and angle of minimum deviation. Finally, you will learn how optical instruments work: the simple microscope, the compound microscope and refracting and reflecting telescopes, with their ray diagrams and magnifying powers.

Detailed Worksheet: Ray Optics and Optical Instruments Section A - Definitions (10 marks) 1. State the Cartesian sign convention for spherical mirrors and lenses. (2 marks) 2. What is total internal reflection? State two conditions for it. (2 marks) 3. Define the power of a lens. Write its SI unit. (2 marks) 4. Define angle of minimum deviation for a prism. (2 marks) 5. Define the magnifying power of a compound microscope and of an astronomical telescope. (2 marks) Section B - Calculations and Applications (15 marks) 6. An object is placed 25 cm in front of a concave mirror of focal length 15 cm. Find the position, nature and magnification of the image. (3 marks) 7. A coin lies at the bottom of a tank filled with water to a depth of 12 cm. Find the apparent depth of the coin and the apparent shift (refractive index of water = 4/3). (3 marks) 8. Find the critical angle for glass of refractive index 1.5 in contact with air (sin 41.8 degrees = 0.667). Explain why a glass prism with angles 45, 45 and 90 degrees can reflect light totally. (3 marks) 9. An object is placed 30 cm from a convex lens of focal length 20 cm. Find the position and magnification of the image and the power of the lens. (3 marks) 10. A double convex lens is made of glass of refractive index 1.5 with radii of curvature 10 cm and 15 cm. Find its focal length using the lens maker's formula. (3 marks) Section C - Diagrams (10 marks) 11. Draw a labelled ray diagram of a compound microscope forming the final image at the least distance of distinct vision. (4 marks) 12. Draw a ray diagram showing refraction of light through a triangular prism, marking the angle of incidence, angle of emergence, angle of the prism and angle of deviation. (3 marks) 13. Draw a labelled diagram of an optical fibre showing total internal reflection of light inside the core. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. (i) Two thin lenses of focal lengths +10 cm and -20 cm are placed in contact. Find the focal length and power of the combination. (ii) A prism of angle 60 degrees gives a minimum deviation of 30 degrees. Find its refractive index. (5 marks) 15. A compound microscope has an objective of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by 15 cm. How far from the objective should an object be placed so that the final image is at 25 cm from the eye? Find the magnifying power. (5 marks) 16. An astronomical telescope has an objective of focal length 140 cm and an eyepiece of focal length 5.0 cm. Find its magnifying power and length in normal adjustment, and its magnifying power when the final image is at 25 cm. State two advantages of reflecting telescopes over refracting ones. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use the Cartesian sign convention throughout and draw ray diagrams with arrows.